Find the ordered pairs for the x - and y-intercepts of the equation 5x - 6y = 30 and select the appropriate option below.

a. The x-intercept is (6, 0), the y-intercept is (0, - 5).

b. The x-intercept is (0, 6); the y-intercept is (-5, 0).

c. The x-intercept is (5, 0); the y-intercept is (0, - 6).

d. The x-intercept is (0, 5); the y-intercept is (-6, 0).

Finding the x-intercept

Since it lies on the x-axis, we know that y=0. Let's plug this into our equation.

5x - 6 (0) = 30

Let's solve for x.

5x - 0 = 30

5x = 30

Divide each side by 5.

x = 6

Our x-intercept is at (6, 0).

Finding the y-intercept

Since it lies on the y-axis, we know that x=0. Let's plug this into our equation.

5 (0) - 6y = 30

Let's solve for x.

0 - 6y = 30

-6y = 30

Divide each side by - 6.

y = - 5

Our y-intercept is at (0, - 5).

Final answer: a. The x-intercept is (6, 0); the y-intercept is (0, - 5).